An OFDM scheme has been considered so as to transmit wideband high-speed data. The OFDM scheme transmits a using bandwidth by dividing the using band into a plurality of subcarriers. The OFDM scheme may provide channel selectivity between separated subcarriers using a wideband channel, and accordingly, such channel diversity may improve performance of a channel encoder. The liner precoding may obtain diversity in a demodulator by multiplying a liner complex matrix by a transmit signal transmitted through the plurality of subcarriers. A paper “Signal Space Diversity: A Power- and Bandwidth-Efficient Diversity Technique for the Rayleigh Fading Channel” discloses a liner complex design method for obtaining the maximum channel diversity, which is published in the IEEE Transactions on Information Theory (Boutros etc., 1998. 6). For example, the OFDMA system using n-numbered (n is a natural number greater than 1) subcarriers may perform a modeling as Equation 1 by using this liner precoding.
                              [                                                                      y                  1                                                                                                      y                  2                                                                                    ⋮                                                                                      y                  n                                                              ]                =                                            [                                                                                          h                      1                                                                            0                                                        …                                                        0                                                                                        0                                                                              h                      2                                                                            ⋱                                                        ⋮                                                                                        ⋮                                                        ⋱                                                        ⋱                                                        0                                                                                        0                                                        …                                                        0                                                                              h                      n                                                                                  ]                        ⁢                                          U                n                            ⁡                              [                                                                                                    x                        1                                                                                                                                                x                        2                                                                                                                        ⋮                                                                                                                          x                        n                                                                                            ]                                              +                      [                                                                                w                    1                                                                                                                    w                    2                                                                                                ⋮                                                                                                  w                    n                                                                        ]                                              (                  Equation          ⁢                                          ⁢          1                )            
When it is given that 1≦i≦n, xi is given as a transmit signal of Binary Phase Shift Keying (BPSK), Quadrature Phase Shift Keying (QPSK), 16 Quadrature Amplitude Modulation (16QAM), and 64QAM etc., and hi is given as a channel for each subcarrier. yi is given as a receive signal. wi is a noise added to the receive signal. In Equation 1, the maximum diversity gain may be obtained by designing well n×n of a liner complex matrix Un.
Generally, it is difficult for the maximum likelihood detection to be applied to the liner precoding system. The maximum likelihood symbol may be detected by applying a Sphere Decoding to a deformed channel matrix when a product of the channel matrix and the liner complex matrix Un is given as the deformed channel matrix, and a performance approaching the maximum likelihood may be detected by a liner receiver (Zero Forcing detection or MMSE detection) after applying the lattice reduction to the deformed channel matrix. A paper “A Very Efficient Lattice Reduction Tool on Fast Fading Channels” published in the International Symposium on Information Theory and its Applications (Rekaya, etc., 2004. 10) discloses an algebraic lattice reduction scheme capable of simply being applied to the precoding system by using the algebraically designed liner complex matrix.
The liner precoding is applied to the OFDMA system so as to obtain frequency diversity on demodulation, while the multiple antennas are applied to the OFDMA system so as to obtain space diversity. A paper “A Simple Transmit Diversity Technique for Wireless Communications” published in the IEEE Journal on Select Areas in Communications (Alamouti, 1998. 10) discloses a space time block code (STBC) design. The space time block code is designed to obtain a diversity gain because a receiver may simply process a signal when two transmit antennas are used and two transmit signals are transmitted using a complex orthogonal design. Such a space time block code may be easily connected to the OFDMA system when they are transmitted over two times for each subcarrier or transmitted over two adjacent subcarriers.
In addition, a paper “Multi-carrier Delay Diversity Modulation for MIMO Systems” published in the IEEE Transaction on Wireless Communications (Tan etc. 2004. 9) discloses that such a space time block code is transmitted with a predetermined delay provided by a time domain for the respective multiple transmit antennas, and accordingly a diversity may be obtained in the frequency domain, and performance may be improved using the channel encoder. At this time, the same receiver as when using one single transmit antenna may be used.
To summarize, the liner precoded multi-carrier system is designed to obtain a frequency diversity gain. In addition, the space time block codes (STBC) are designed to obtain a space diversity gain. The delay diversity applied to the multi-carrier system is designed to obtain a gain by deforming space diversity into frequency diversity.
However, the conventional multi-carrier system has bad performance because the space diversity using the multiple antennas and the frequency diversity using the OFDMA system are used together. Also, it undergoes performance degradation because the lattice reduction detection method has a boundary effect, and accordingly, severe fading occurs on the radio channel.
The above information disclosed in this Background section is only for enhancement of understanding of the background of the invention and therefore it may contain information that does not form the prior art that is already known in this country to a person of ordinary skill in the art.